I worked in the actuarial field for 23 years, specializing in personal auto insurance. Some states are like the ones you described ("prior approval"). But others did not require prior approval of rate changes. Those were called "file and use" states. I don't recall the exact breakdown between these two broad groups, but I can say that the states where car insurance was more expensive in general tended to be prior approval ones. Those states asked us the most questions and gave us the hardest time before they would grant approvals.
As for my own car, the rates dropped a lot during COVID. This was for liability coverages (which did not depend on aging of my car) and for physical damage coverages (Comprehensive and Collision) whose rates dropped also due to the car aging.
But with COVID behind us, at least as far as car insurance goes, the rates for my liability coverages have risen pretty sharply this year, back to pre-COVID levels, while physical damage coverages have risen slightly, as opposed to still dropping due to the car's aging. Physical Damage rates, for me, are only about 20% of the total premium.